defines a probability measure on \(A_{\mathbf {I}}\) . The exact-dimensionality of \(\Phi _{\mathbf {I}}(\mu ^+)\)  was proved by Feng and Hu [1]}, and in our notation the dimension is equal to
\(\dim \Phi _{\mathbf {I}}(\mu )=\frac{h_\mu -h_{\mu ,\mathbf {I}}}{\chi _{\mu ,\mathbf {I}}},\) 
